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The Random Feature Model for Input-Output Maps between Banach Spaces

20 May 2020

Papers citing "The Random Feature Model for Input-Output Maps between Banach Spaces"

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Title
LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE Siwen Zhang Xizeng Zhao Zhengzhi Deng Zhaoyuan Huang Gang Tao Nuo Xu Zhouteng Ye 68 0 0 18 May 2025
On the choice of the non-trainable internal weights in random feature maps Pinak Mandal Georg Gottwald Nicholas Cranch TPM 89 1 0 07 Aug 2024
Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features Oliver R. A. Dunbar Nicholas H. Nelsen Maya Mutic 147 7 0 30 Jun 2024
Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective Samuel Lanthaler 91 4 0 26 Jun 2024
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators Gianluca Fabiani Ioannis G. Kevrekidis Constantinos Siettos A. Yannacopoulos 104 13 0 08 Jun 2024
A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks Graham Pash M. Hassanaly S. Yellapantula AI4CE 85 0 0 28 Feb 2024
Learning About Structural Errors in Models of Complex Dynamical Systems Jin-Long Wu Matthew E. Levine Tapio Schneider Andrew M. Stuart AI4CE 82 18 0 29 Dec 2023
Diffusion Random Feature Model Esha Saha Giang Tran DiffM 70 0 0 06 Oct 2023
Energy-Dissipative Evolutionary Deep Operator Neural Networks Jiahao Zhang Shiheng Zhang Jie Shen Guang Lin 51 12 0 09 Jun 2023
Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators Dingcheng Luo Thomas O'Leary-Roseberry Peng Chen Omar Ghattas AI4CE 83 16 0 31 May 2023
Nonlocality and Nonlinearity Implies Universality in Operator Learning S. Lanthaler Zong-Yi Li Andrew M. Stuart 75 17 0 26 Apr 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 72 26 0 28 Mar 2023
RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator Xiaoyu Zhao Xiaoqian Chen Zhiqiang Gong Weien Zhou Wen Yao Yunyang Zhang AI4CE 68 24 0 20 Feb 2023
A Neural PDE Solver with Temporal Stencil Modeling Zhiqing Sun Yiming Yang Shinjae Yoo DiffM AI4CE 98 17 0 16 Feb 2023
Score-based Diffusion Models in Function Space Jae Hyun Lim Nikola B. Kovachki Ricardo Baptista Christopher Beckham Kamyar Azizzadenesheli ... Karsten Kreis Jan Kautz Christopher Pal Arash Vahdat Anima Anandkumar DiffM 193 50 0 14 Feb 2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs Ke Chen Chunmei Wang Haizhao Yang AI4CE 68 14 0 28 Jan 2023
Koopman neural operator as a mesh-free solver of non-linear partial differential equations Wei Xiong Xiaomeng Huang Ziyang Zhang Ruixuan Deng Pei Sun Yang Tian AI4CE 78 35 0 24 Jan 2023
Non-equispaced Fourier Neural Solvers for PDEs Haitao Lin Lirong Wu Yongjie Xu Yufei Huang Siyuan Li Guojiang Zhao Z. Stan 76 8 0 09 Dec 2022
Catch-22s of reservoir computing Yuanzhao Zhang Sean P. Cornelius 89 13 0 18 Oct 2022
Transformer Meets Boundary Value Inverse Problems Ruchi Guo Shuhao Cao Long Chen MedIm 124 23 0 29 Sep 2022
$Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator$ Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator Ming Zhong Zhenya Yan 29 17 0 29 Aug 2022
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs Emilia Magnani Nicholas Kramer Runa Eschenhagen Lorenzo Rosasco Philipp Hennig UQCV BDL 62 13 0 02 Aug 2022
Semi-supervised Learning of Partial Differential Operators and Dynamical Flows Michael Rotman A. Dekel R. Ber Lior Wolf Yaron Oz AI4CE 25 4 0 28 Jul 2022
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning Thomas O'Leary-Roseberry Peng Chen Umberto Villa Omar Ghattas AI4CE 102 42 0 21 Jun 2022
NOMAD: Nonlinear Manifold Decoders for Operator Learning Jacob H. Seidman Georgios Kissas P. Perdikaris George J. Pappas AI4CE 103 78 0 07 Jun 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 117 172 0 26 May 2022
STONet: A Neural-Operator-Driven Spatio-temporal Network Haitao Lin Guojiang Zhao Lirong Wu Stan Z. Li AI4TS AI4CE 70 1 0 18 Apr 2022
Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs Tailin Wu Qi Meng Bin Chen Shiqi Gong Yue Wang Wei Chen Rongchan Zhu Zhirui Ma Tie-Yan Liu AI4CE 86 11 0 13 Apr 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 95 175 0 12 Feb 2022
Towards Empirical Process Theory for Vector-Valued Functions: Metric Entropy of Smooth Function Classes Junhyung Park Krikamol Muandet 73 10 0 09 Feb 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 86 113 0 04 Jan 2022
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks Thomas O'Leary-Roseberry Xiaosong Du A. Chaudhuri J. Martins Karen E. Willcox Omar Ghattas 66 23 0 14 Dec 2021
Variational Regularization in Inverse Problems and Machine Learning Martin Burger 18 3 0 08 Dec 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 127 427 0 06 Nov 2021
Convergence Rates for Learning Linear Operators from Noisy Data Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart 171 58 0 27 Aug 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 95 19 0 26 Aug 2021
Neural Operator: Learning Maps Between Function Spaces Nikola B. Kovachki Zong-Yi Li Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 170 453 0 19 Aug 2021
Learning the optimal Tikhonov regularizer for inverse problems Giovanni S. Alberti Ernesto De Vito Matti Lassas Luca Ratti Matteo Santacesaria 69 30 0 11 Jun 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 88 256 0 31 May 2021
Two-layer neural networks with values in a Banach space Yury Korolev 95 24 0 05 May 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 84 157 0 24 Mar 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 104 715 0 19 Mar 2021
Reduced operator inference for nonlinear partial differential equations E. Qian Ionut-Gabriel Farcas Karen E. Willcox AI4CE 53 39 0 29 Jan 2021
DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems Craig Gin D. Shea Steven L. Brunton J. Nathan Kutz 82 90 0 31 Dec 2020
Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM Oliver R. A. Dunbar A. Garbuno-Iñigo T. Schneider Andrew M. Stuart 86 60 0 24 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 554 2,465 0 18 Oct 2020
A Kernel Two-Sample Test for Functional Data George Wynne Andrew B. Duncan 88 45 0 25 Aug 2020
Understanding Recurrent Neural Networks Using Nonequilibrium Response Theory Soon Hoe Lim 81 16 0 19 Jun 2020
Multipole Graph Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 230 395 0 16 Jun 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 102 83 0 25 Apr 2020